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The 3D Estimator: Introducing Middle-School Students to Back of the Envelope Estimation Interactively

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2013 ASEE Annual Conference & Exposition


Atlanta, Georgia

Publication Date

June 23, 2013

Start Date

June 23, 2013

End Date

June 26, 2013



Conference Session

K-12 and Pre-College Engineering Poster Session

Tagged Division

K-12 & Pre-College Engineering

Page Count


Page Numbers

23.1165.1 - 23.1165.15



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Paper Authors


Peter Thomas Malcolm University of Virginia

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Peter T. Malcolm is a graduate research assistant in the Curry School of Education at the University of Virginia in Charlottesville. His primary interest is in developing software to help elementary and middle school students visualize, understand, and interact with STEM concepts.

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The Spatial Estimator: Design Feedback and the Fundamental Engineering Abilities of Mental Rotation and ApproximationThe White House has called educators to action around "science, technology, engineering andmath" ([STEM] Obama, 2010) in K-12 schools in the U.S. Meanwhile the absence of the "e" inSTEM from the traditional American curriculum is being remedied by the movement tostandardize engineering knowledge for pre-college learners (NAE, 2010). There are several keyprerequisites to engineering learning, and this paper addresses ways of teaching two thesefundamental prerequisite abilities in middle school. The abilities addressed here are: (1) mentalrotation ability, often included among a more broad set of spatial skills (Sorby, 2009) and (2) theability to make multi-step estimates. The research proposed is situated in project-basedenvironment for digital fabrication.Mental rotation ability predicts a host of engineering abilities and has been found to be mutableand teachable (Sorby, 2009). This is the ability to mentally rotate shapes and to imagine them indifferent orientations. Chemical, mechanical, and even software engineers use this ability.Numerical approximation (estimation) is a ubiquitous skill (Usiskin, 1986) used mostly in theearly stages of a project. For example, establishing feasibility depends upon using estimates.Erico Fermi (1901-1954) coined the term "back of the envelope" to refer to large estimates basedon a series of smaller estimates. These so-called Fermi problems are useful in engineeringeducation (e.g., Barak, Raviv & VanEpps, 2009; Dunn-Rankin, 2001; French & Leiffer, 2012).The Spatial Estimator is a new online tool designed to help students estimate properties of three-dimensional shapes as an early step in digital fabrication (Bell et al, 2010; Berry et al., 2010).Digital fabrication involves the design and creation of tangible objects by way of digital devices,and can include die-cutting and three-dimensional (3D) printing. As manufacturing becomessmall-scale and computer-aided-design (CAD) programs become more accessible, widespreadeducational uses of digital fabrication have great educational potential. Early research withdigital fabrication in K-12 education shows promise (Tillman, 2011).This research is based on the hypothesis that students can learn to make practical estimates aboutthe amount of time and materials needed for digital fabrication. Feedback in software willencourage students to explore aspects of their own designs to establish properties such as volumeand the necessary density of their materials. Currently, 3D printers must be used judiciously inclassrooms because of the requisite costs of time and access to fabrication materials such asplastic. These real-world constraints can be assets to a teacher since they provide authenticdesign specifications.Students will revise estimates based on interaction with three-dimensional shapes in software.This will require spatial thinking and mental rotation, in addition to the point-and-click rotationof the shapes on screen. Students' iterative estimates will elicit feedback from the computer, andstudent actions will be recorded as log files for analysis. It is anticipated that student estimatesbecome more accurate with practice and that their solutions will benefit from work with theSpatial Estimator.REFERENCES:Bell, B. L., Brown, A., Bull, G., Conly, K., Johnson, L., Mcanear, … Sprague, D., (2010). A special editorial: Digital fabrication revolution, TechTrends 54(5).Berry, R. Q., III, Bull, G., Browning, C., Thomas, C. D., Starkweather, K., & Aylor, J. H. (2010). Preliminary considerations regarding use of digital fabrication to incorporate engineering design principles in elementary mathematics education. Contemporary Issues in Technology and Teacher Education, 10(2). Retrieved from, G., & Groves, J. (2009). The democratization of production. Learning and Leading with Technology, 37(3), 36-37.Dunn-rankin, D. (2001). Evaluating design alternatives – the role of simple engineering analysis and estimation. 2001 ASEE Annual Conference & Exposition.French, J. J., & Leiffer, P. R. (2012). The genesis of transformation: Preventing “failure to launch” syndrome in generation in first-year engineering students. 2012 ASEE Annual Conference & Exposition.Kolodner, J. L., Camp, P. J., Crismond, D., Fasse, B., Gray, J., Holbrook, J., Puntambekar, S., et al. (2003). Problem-based learning meets case-based reasoning in the middle-school science classroom: Putting learning by design™ into practice. Journal of the Learning Sciences, 12(4), 495–547. doi:10.1207/S15327809JLS1204_2Obama, B. (2010). Remarks by the president at the announcement of the “Change the Equation” initiative. Retrieved from the White House Web site: press- office/2010/09/16/remarks - president- announcement- change- equation- initiativeRaviv, D., Barak, M., Sheva, B., Vanepps, T. J., & Raton, B. (2009). Teaching innovative thinking: Future directions. 2009 ASEE Annual Conference & Exposition.Tillman, D. (2011). Performance assessment of digital fabrication activities with embedded mathematics pedagogy. In M. Koehler & P. Mishra (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference 2011 (pp. 898– 901). Chesapeake, VA: AACE.

Malcolm, P. T. (2013, June), The 3D Estimator: Introducing Middle-School Students to Back of the Envelope Estimation Interactively Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--22550

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